Colloque des sciences mathématiques du Québec

17 avril 2009 de 16 h 00 à 18 h 00 (heure de Montréal/Miami) Sur place

Arithmetic Laplacian

Colloque par Alexandru Buium (University of New Mexico)

We develop an arithmetic analogue of elliptic partial differential equations. The role of the space coordinates is played by a family of primes, and that of the space derivatives along the various primes are played by corresponding Fermat quotient operators subjected to certain commutation relations. This leads to arithmetic linear partial differential equations on algebraic groups that are analogues of certain operators in analysis constructed from Laplacians. We classify all such equations on one dimensional groups, in particular on elliptic curves, and analyze their spaces of solutions.

Adresse

Salle 6214, Pavillon André Aisenstadt, 2920 ch. de la Tour, Université de Montréal